Yes, it is possible for a rectangle with a perimeter of 52cm to have an area of 148.75 square centimeters
The perimeter of a rectangle is
P=2(l+w)
The area of a rectangle is,
A=l*w
2(l+w)=52
l+w=26
l=26-w
Now plug that into the area formula,
l*w=148.25
(26-w)*w=148.25
26W-W^2=148.25
W^2-26W+148.25=0
There are two positive solutions.
About W=8 and W=18, which gives L=18 and L=8 respectively or an approximately 8x18 cm rectangle.
So yes, you can have a rectangle of perimeter 52 cm and area of 148.25 sq. cm.
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